{"title":"On analogues of Mazur-Tate type conjectures in the Rankin-Selberg setting","authors":"Antonio Cauchi, Antonio Lei","doi":"10.5565/publmat6622204","DOIUrl":"https://doi.org/10.5565/publmat6622204","url":null,"abstract":"","PeriodicalId":54531,"journal":{"name":"Publicacions Matematiques","volume":" ","pages":""},"PeriodicalIF":1.1,"publicationDate":"2022-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48974425","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
: In this paper, we study the existence and uniqueness of bounded viscosity solutions for parabolic Hamilton–Jacobi monotone systems in which the diffusion term is driven by variable-order nonlocal operators whose kernels depend on the space-time variable. We prove the existence of solutions via Perron’s method, and considering Hamiltonians with linear and superlinear nonlinearities related to their gradient growth we state a comparison principle for bounded sub and supersolutions. Moreover, we present steady-state large time behavior with an exponential rate of convergence.
{"title":"Monotone systems involving variable-order nonlocal operators","authors":"Miguel Yangari","doi":"10.5565/publmat6612205","DOIUrl":"https://doi.org/10.5565/publmat6612205","url":null,"abstract":": In this paper, we study the existence and uniqueness of bounded viscosity solutions for parabolic Hamilton–Jacobi monotone systems in which the diffusion term is driven by variable-order nonlocal operators whose kernels depend on the space-time variable. We prove the existence of solutions via Perron’s method, and considering Hamiltonians with linear and superlinear nonlinearities related to their gradient growth we state a comparison principle for bounded sub and supersolutions. Moreover, we present steady-state large time behavior with an exponential rate of convergence.","PeriodicalId":54531,"journal":{"name":"Publicacions Matematiques","volume":"1 1","pages":""},"PeriodicalIF":1.1,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42681755","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We describe the real forms of Gizatullin surfaces of the form $xy=p(z)$ and of Koras-Russell threefolds of the first kind. The former admit zero, two, three, four or six isomorphism classes of real forms, depending on the degree and the symmetries of the polynomial~$p$. The latter, which are threefolds given by an equation of the form $x^dy+z^k+x+t^ell=0$, all admit exactly one real form up to isomorphism.
{"title":"Real forms of some Gizatullin surfaces and Koras-Russell threefolds","authors":"J. Blanc, A. Bot, Pierre-Marie Poloni","doi":"10.5565/publmat6722314","DOIUrl":"https://doi.org/10.5565/publmat6722314","url":null,"abstract":"We describe the real forms of Gizatullin surfaces of the form $xy=p(z)$ and of Koras-Russell threefolds of the first kind. The former admit zero, two, three, four or six isomorphism classes of real forms, depending on the degree and the symmetries of the polynomial~$p$. The latter, which are threefolds given by an equation of the form $x^dy+z^k+x+t^ell=0$, all admit exactly one real form up to isomorphism.","PeriodicalId":54531,"journal":{"name":"Publicacions Matematiques","volume":" ","pages":""},"PeriodicalIF":1.1,"publicationDate":"2021-08-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48399142","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We describe some new ways to construct saturated fusion subsystems, including, as a special case, the normalizer of a set of components of the ambient fusion system. This was motivated in part by Aschbacher's construction of the normalizer of one component, and in part by joint work with three other authors where we had to construct the normalizer of all of the components.
{"title":"Normalizers of sets of components in fusion systems","authors":"B. Oliver","doi":"10.5565/publmat6722312","DOIUrl":"https://doi.org/10.5565/publmat6722312","url":null,"abstract":"We describe some new ways to construct saturated fusion subsystems, including, as a special case, the normalizer of a set of components of the ambient fusion system. This was motivated in part by Aschbacher's construction of the normalizer of one component, and in part by joint work with three other authors where we had to construct the normalizer of all of the components.","PeriodicalId":54531,"journal":{"name":"Publicacions Matematiques","volume":" ","pages":""},"PeriodicalIF":1.1,"publicationDate":"2021-07-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47356853","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We study the structure of groups of finite (Pr¨ufer) rank in a very wide class of groups and also of central extensions of such groups. As a result we are able to improve, often substantially, on a number of known numerical bounds, in particularon bounds for the rank (resp. Hirsch number) of the derived subgroup of a group in terms of the rank (resp. Hirsch number) of its central quotient and on bounds for the rank of a group in terms of its Hirsch number
{"title":"On groups of finite rank","authors":"B. Wehrfritz","doi":"10.5565/PUBLMAT6522106","DOIUrl":"https://doi.org/10.5565/PUBLMAT6522106","url":null,"abstract":"We study the structure of groups of finite (Pr¨ufer) rank in a very wide class of groups and also of central extensions of such groups. As a result we are able to improve, often substantially, on a number of known numerical bounds, in particularon bounds for the rank (resp. Hirsch number) of the derived subgroup of a group in terms of the rank (resp. Hirsch number) of its central quotient and on bounds for the rank of a group in terms of its Hirsch number","PeriodicalId":54531,"journal":{"name":"Publicacions Matematiques","volume":" ","pages":""},"PeriodicalIF":1.1,"publicationDate":"2021-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42143173","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
A. Avil'es, G. Mart'inez-Cervantes, Abraham Rueda Zoca
A result of G. Godefroy asserts that a Banach space $X$ contains an isomorphic copy of $ell_1$ if and only if there is an equivalent norm $|||cdot|||$ such that, for every finite-dimensional subspace $Y$ of $X$ and every $varepsilon>0$, there exists $xin S_X$ so that $|||y+r x|||geq (1-varepsilon)(|||y|||+vert rvert)$ for every $yin Y$ and every $rinmathbb R$. In this paper we generalize this result to larger cardinals, showing that if $kappa$ is an uncountable cardinal then a Banach space $X$ contains a copy of $ell_1(kappa)$ if and only if there is an equivalent norm $|||cdot|||$ on $X$ such that for every subspace $Y$ of $X$ with $dens(Y)
{"title":"A renorming characterization of Banach spaces containing $ell_1 (kappa)$","authors":"A. Avil'es, G. Mart'inez-Cervantes, Abraham Rueda Zoca","doi":"10.5565/publmat6722305","DOIUrl":"https://doi.org/10.5565/publmat6722305","url":null,"abstract":"A result of G. Godefroy asserts that a Banach space $X$ contains an isomorphic copy of $ell_1$ if and only if there is an equivalent norm $|||cdot|||$ such that, for every finite-dimensional subspace $Y$ of $X$ and every $varepsilon>0$, there exists $xin S_X$ so that $|||y+r x|||geq (1-varepsilon)(|||y|||+vert rvert)$ for every $yin Y$ and every $rinmathbb R$. In this paper we generalize this result to larger cardinals, showing that if $kappa$ is an uncountable cardinal then a Banach space $X$ contains a copy of $ell_1(kappa)$ if and only if there is an equivalent norm $|||cdot|||$ on $X$ such that for every subspace $Y$ of $X$ with $dens(Y)<kappa$ there exists a norm-one vector $x$ so that $||| y+r x|||=|||y|||+vert rvert$ whenever $yin Y$ and $rinmathbb{R}$. This result answers a question posed by S. Ciaci, J. Langemets and A. Lissitsin, where the authors wonder whether the previous statement holds for infinite succesor cardinals. We also show that, in the countable case, the result of Godefroy cannot be improved to take $varepsilon=0$.","PeriodicalId":54531,"journal":{"name":"Publicacions Matematiques","volume":" ","pages":""},"PeriodicalIF":1.1,"publicationDate":"2021-04-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42407759","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Let F be a global function field of characteristic p with ring of integers A and let Phi be a Hayes module on the Hilbert class field H(A) of F. We prove an Iwasawa Main Conjecture for the Z_p^infty-extension F/F generated by the mathfrak{p}-power torsion of Phi (mathfrak{p} a prime of A). The main tool is a Stickelberger series whose specialization provides a generator for the Fitting ideal of the class group of F. Moreover we prove that the same series, evaluated at complex or p-adic characters, interpolates the Goss Zeta-function or some p-adic L-function, thus providing the link between the algebraic structure (class groups) and the analytic functions, which is the crucial part of Iwasawa Main Conjecture.
{"title":"Stickelberger series and Main Conjecture for function fields","authors":"A. Bandini, E. Coscelli","doi":"10.5565/PUBLMAT6522103","DOIUrl":"https://doi.org/10.5565/PUBLMAT6522103","url":null,"abstract":"Let F be a global function field of characteristic p with ring of integers A and let Phi be a Hayes module on the Hilbert class field H(A) of F. We prove an Iwasawa Main Conjecture for the Z_p^infty-extension F/F generated by the mathfrak{p}-power torsion of Phi (mathfrak{p} a prime of A). The main tool is a Stickelberger series whose specialization provides a generator for the Fitting ideal of the class group of F. Moreover we prove that the same series, evaluated at complex or p-adic characters, interpolates the Goss Zeta-function or some p-adic L-function, thus providing the link between the algebraic structure (class groups) and the analytic functions, which is the crucial part of Iwasawa Main Conjecture.","PeriodicalId":54531,"journal":{"name":"Publicacions Matematiques","volume":"1 1","pages":""},"PeriodicalIF":1.1,"publicationDate":"2021-03-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41336489","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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